Undergraduate Students’ Cognitive Obstacles in the Learning Power Series Concepts Using APOS

Abstract

Power series are a powerful tool to study elementary functions that are widely used in computational sciences to obtain approximations of functions. However, students do not fully develop required mental structures due to the presence of cognitive obstacles. The purpose of this study was to develop students’ mental constructions in learning power series expansion using the activities, whole class discussions and exercises instructional approach. Literature on the activities, class discussion and exercise instructional approach in power series is scarce. This framework advocates for the use activities, class discussion and exercises teaching cycles to develop undergraduate students’ mental constructions in mathematics concepts. A qualitative case study research approach involving 101 first-year undergraduate students was adopted for this study. Students’ understanding of power series expansion was gathered by using a task-sheet and semi-structured interviews. Data analysis consisted of content analysis of students’ written responses to the exercises and identify categories. The results indicated that students partially developed the schema for expanding power series and solving related problems. Students had some content gaps in the pre-schemas, which in true became some cognitive obstacles in learning power series. Future studies may focus on mental constructions and obstacles in other aspects of series expansion.